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Category: Integration

d-3x-x-7-

Question Number 18889 by Joel577 last updated on 01/Aug/17 $$\int\:\frac{{d}\left(\sqrt{\mathrm{3}{x}}\right)}{\:\sqrt{\sqrt{{x}}\:+\:\mathrm{7}}} \\ $$ Commented by Joel577 last updated on 01/Aug/17 $$\mathrm{I}\:\mathrm{got}\:\mathrm{2}\sqrt{\mathrm{3}\left(\sqrt{{x}}\:+\:\mathrm{7}\right)}\:+\:{C} \\ $$$$\mathrm{is}\:\mathrm{it}\:\mathrm{correct}? \\ $$ Commented…

x-4-x-2-dx-

Question Number 84415 by TawaTawa1 last updated on 12/Mar/20 $$\int\:\sqrt{\mathrm{x}\:−\:\sqrt{\mathrm{4}\:−\:\mathrm{x}^{\mathrm{2}} }}\:\:\mathrm{dx} \\ $$ Answered by john santu last updated on 13/Mar/20 $$\mathrm{let}\:\mathrm{x}\:=\:\mathrm{2sin}\:\mathrm{t} \\ $$$$\int\:\sqrt{\mathrm{2sin}\:\mathrm{t}−\mathrm{2cos}\:\mathrm{t}}\:×\mathrm{2cos}\:\mathrm{t}\:\mathrm{dt} \\…

x-x-1-x-2-dx-

Question Number 84396 by Aditya789 last updated on 12/Mar/20 $$\int\frac{\mathrm{x}\sqrt{\mathrm{x}+\mathrm{1}}}{\mathrm{x}+\mathrm{2}}\mathrm{dx} \\ $$ Commented by jagoll last updated on 12/Mar/20 $$\mathrm{let}\:\sqrt{\mathrm{x}+\mathrm{1}\:}\:=\:\mathrm{u}\:\Rightarrow\:\mathrm{x}=\mathrm{u}^{\mathrm{2}} −\mathrm{1} \\ $$$$\Rightarrow\int\:\frac{\:\:\left(\mathrm{u}^{\mathrm{2}} −\mathrm{1}\right)\mathrm{u}\:\left(\mathrm{2u}\:\mathrm{du}\right)}{\mathrm{u}^{\mathrm{2}} +\mathrm{1}}\:=\:…

x-4-x-2-dx-

Question Number 84386 by M±th+et£s last updated on 12/Mar/20 $$\int\sqrt{{x}−\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }}\:{dx} \\ $$ Answered by mind is power last updated on 13/Mar/20 $${x}=\mathrm{2}{sin}\left({t}\right)\Rightarrow \\ $$$$=\int\mathrm{2}{cos}\left({t}\right)\sqrt{\mathrm{2}{sin}\left({t}\right)−\mathrm{2}{cos}\left({t}\right)}{dt}\:\:{let}…

Question-84379

Question Number 84379 by Power last updated on 12/Mar/20 Answered by mind is power last updated on 12/Mar/20 $$=\int\frac{{x}\mathrm{2}{i}}{{e}^{{ix}} −{e}^{−{ix}} }{dx} \\ $$$$=\int\frac{{x}\mathrm{2}{ie}^{{ix}} }{\left({e}^{\mathrm{2}{ix}} −\mathrm{1}\right)}{dx}={f}\left({x}\right)…

0-pi-2-cos-3-x-1-cos-2-x-dx-

Question Number 149903 by bramlexs22 last updated on 08/Aug/21 $$\:\Omega\:=\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}}{\:\sqrt{\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}}\:\mathrm{dx}\: \\ $$ Answered by Ar Brandon last updated on 08/Aug/21 $$\Omega=\int_{\mathrm{0}}…